Finite Group Databasebeta

← #15773653

Subgroups — #15773653

Order 3328.

434 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114916C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic
3#13112863C214yesmaximal, complemented
4C2×C13×#400C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C13×#400—21no—
8C13×#400—21no—
9C13×#400C412yes—
10C13×#400C2212yes—
11C2×C13×#95—21no—
12C2×C13×#95—21no—
13C2×C13×#95C411yescharacteristic
14#11718868—21no—
15#11718868—21no—
16#11718122—21no—
17#11718122C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C23×C4×C13—21no—
21C23×C4×C13—21no—
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—41no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×#6099—22no—
36C2×#6099—41no—
37C13×#95—21no—
38C13×#95—22no—
39C13×#95—22no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95C2×C412yes—
43C22⋊#1055—22no—
44C22⋊#1055—41no—
45C22⋊#1055—41no—
46C22⋊#1055—41no—
47#11814—131nomaximal, Sylow
48C24×C13C22⋊C411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—44no—
64C22×C4×C13—42no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79#6099—42no—
80#6099—42no—
81#6099—82no—
82C2×#1055—42no—
83C2×#1055—42no—
84C2×#400D1311yescharacteristic
85#1821—131no—
86#1463—131no—
87#1353—134no—
88C23×C13—22no—
89C23×C13—22no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13#9911yescharacteristic
93C23×C13#9911yescharacteristic
94C23×C13C2×C22⋊C411yescharacteristic
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—44no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—81no—
119C2×C4×C13—84no—
120C2×C4×C13—82no—
121C2×C4×C13—82no—
122C2×C4×C13#13712yes—
123#1055—82no—
124#1055—82no—
125C22×C4⋊C4Dic1311yescharacteristic
126C22×C4⋊C4C2×D1311yescharacteristic
127#407—261no—
128#407—261no—
129#400—21no—
130#400—21no—
131#400Dic1312yes—
132#400C2×D1312yes—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95Dic1311yescharacteristic
136#343—132no—
137#343—261no—
138#324—132no—
139#324—261no—
140C22×C13—24no—
141C22×C13—24no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13#35212yes—
149C22×C13#35512yes—
150C22×C13C2×#9911yescharacteristic
151C22×C13#41911yescharacteristic
152C22×C13#42111yescharacteristic
153C4×C13—22no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—82no—
160C4×C13—82no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4C2×Dic1311yescharacteristic
164C23×C4C22⋊D1311yescharacteristic
165C23×C4C22⋊D1311yescharacteristic
166C2×M16—262no—
167C2×M16—521no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4C2×Dic1312yes—
174C2×C4⋊C4C2×Dic1311yescharacteristic
175C2×C4⋊C4C22⋊D1311yescharacteristic
176C2×C4⋊C4C22⋊D1311yescharacteristic
177C2×C4⋊C4C22×D1311yescharacteristic
178C22⋊C8—262no—
179C22⋊C8—521no—
180C22⋊C8—521no—
181C22⋊C8—521no—
182#95—22no—
183#95—22no—
184#95—21no—
185#95—22no—
186#95—22no—
187#95C2×Dic1312yes—
188C2×C13—21no—
189C2×C13—22no—
190C2×C13—22no—
191C2×C13—21no—
192C2×C13#151111yescharacteristic
193C2×C13C2×#35211yescharacteristic
194C2×C13C2×#35511yescharacteristic
195C24C22⋊Dic1311yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—41no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—44no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4C22⋊Dic1311yescharacteristic
215C22×C4C22⋊Dic1311yescharacteristic
216C22×C4C22⋊Dic1311yescharacteristic
217C22×C4C22×Dic1311yescharacteristic
218C22×C4C2×C22⋊D1311yescharacteristic
219C22×C4C2×C22⋊D1311yescharacteristic
220M16—522no—
221M16—522no—
222M16—1042no—
223C2×C8—522no—
224C2×C8—522no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C13#1181411yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—22no—
235C23—22no—
236C23#8807411yescharacteristic
237C23#8807411yescharacteristic
238C23C2×C22⋊Dic1311yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—84no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4#8819612yes—
267C8—1042no—
268C8—1042no—
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#1171813112yes—
278C22#1171813412yes—
279C22C2×#8807411yescharacteristic
280C22#1171888611yescharacteristic
281C22#1171889711yescharacteristic
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—82no—
289C4—82no—
290C2—21no—
291C2—21no—
292C2—22no—
293C2—22no—
294C2#1311336911yescharacteristic
295C2C2×#1171813111yescharacteristic
296C2C2×#1171813411yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#400C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#400D13
hypocenterC13#11814
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#400

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13112863C2semidirect
231. C13#11814semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131149162
#131131662
#131128632
C2×C13×#4002
#1181413